A fair die is thrown until a number less than five is obtained. The probability of obtaining a number less than three on the last throw is :
Answers
Answer:
This just says that a throw is less than 5, that is, 1, 2, 3, or 4. We are asked for the probability of less than 3, that is, 1 or 2, given that it is 1, 2, 3, or 4. We should not need theory to see that the probability is 2/4.
Effectively, the condition "less than 5" restricts the sample space to 4 equally likely outcomes.
We can set it up and solve it as a formal conditional probability problem. Let A be the event "less than 3" and B be the event "less than 5." We want P(A|B). Since P(A|B)P(B)=P(A∩B), we need only compute P(B) and P(A∩B). Easily, the probability that a thrrow is less than 5 is 4/6. Also, P(A∩B) is just P(A), which is 2/6.
Remark: It is important not to be distracted by the irrelevant detail that there may have been a long string of 5's and/or 6's before the crucial throw. One could also do the computation by taking into account these irrelevant throws. More work, with result, when the smoke clears, 1/2.